Geometrisation of Ohm's reciprocity relation in a holographic plasma

TL;DR

This paper demonstrates that the reciprocity relation between conductivity and resistivity can be geometrically understood in certain holographic theories, showing their equivalence in electric transport properties through duality and numerical validation.

Contribution

It proves a geometrical interpretation of Ohm's reciprocity in holographic theories and establishes their equivalence in electric transport via a generalized electric-magnetic duality.

Findings

Reciprocity relation holds in specific holographic models.

Duality leads to suppression of electromagnetic contributions to transport.

Numerical simulations confirm theoretical predictions.

Abstract

It has been recently pointed out that the familiar reciprocity relation between the conductivity $\sigma$ and resistivity $\rho$, which I refer to as $\textit{Ohm's reciprocity relation}$, should not be expected to hold in all possible settings, but is rather a property that may (or may not) emerge as a consequence of specific features, or in certain limits of interest, of a given theory. In this work I prove an analogous statement: $\rho= \sigma^{-1}$, across two different classes of holographic theories related by a generalisation of the electric-magnetic duality in the $D=4+1$ bulk. In terms of the dual hydrodynamic theories, this statement is shown to imply the suppression of any contributions to the transport coefficients from dynamical electromagnetic fields, present in only one of the two theories. This makes the two theories, as far as late-time linear electric transport is concerned, equivalent. I then confirm these findings by considering one specific model and run numerical simulations in different settings.